I've always felt "reproduction" was a more appropriate and more definitive term, even though I don’t think that term will ever catch on. When I hear "kit car”, I think back to when you would take a Volkswagen Beetle, remove the body, and replace it with an older Mercedes aftermarket body that came with a “kit” built just for that purpose. Our Cobras, even if not “real” or “original” are built from the ground up to be just what they are.
You don't hear the term “kit” or even "replica" used when people build a '60s Mustang or Camaro using essentially all aftermarket body panels, frames, suspensions, interiors, etc. They are all referred to as "reproduction" pieces. Even if they are steel instead of fiberglass, it's a remake of the original. I don't think you will see the terms "replica" or "kit" used on the Dynacorn website where they sell all of these pieces for those vehicles, just "reproduction".
With that being said, as others have said, just take their interest as a compliment and tell them all they want to know about the car. If they try to steer the conversation towards what to call it, just politely bow out of the conversation and tell them you have to be somewhere, and watch how they watch, and listen, with envy as you drive off.
Here’s a thread with way more discussion on this topic…
New name for "Replicas"